University of TehranSchool of Electrical and Computer Engineering

Center of Excellence forControl and Intelligent Processing

Designing MIMO PID Controller using Colonial Competitive Algorithm: Applied

to Distillation Column Process

By:Esmaeil Atashpaz Gargari

Farzad HashemzadehCaro Lucas

Control and Intelligent Processing Center of Excellence, University of Tehran, Tehran, Iran

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Introduction Outline

Main objectivePID Controller for Multivariable ProcessProblem StatementWhat is Colonial Competitive Algorithm

(CCA)?Simulation ResultsConclusion

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Introduction Main objective

To show an industrial application of a novel evolutionary optimization algorithm.

To design a MIMO PID controller for a distillation column process

The design objective in PID controller design is to track the system outputs by the inputs.

A colonial competitive Algorithm is used for this purpose.

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PID Controller for Multivariable Process

11 1

1

( ) ( )

( )

( ) ( )

n

n nn

p s p s

s

p s p s

P

1 2[ ]T

d d d dny y yY

1 2[ ]T

ny y yY

1 2[ ]T

nu u uU

11 22[ ]T

d nne e e E Y Y

11 1

1

( ) ( )

( )

( ) ( )

n

n nn

c s c s

s

c s c s

C

01 1

( )n n

ij

i j

IAE e t dt

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What is Colonial Competitive Algorithm? Introduction

Colonial Competitive Algorithm (CCA) is novel socio-politically motivated optimization strategy.

Proposed by Atashpaz-gargari and Lucas in the papers“Imperialist Competitive Algorithm: An Algorithm for Optimization Inspired by Imperialistic Competition”. IEEE CEC 2007, Singapore

Is inspired by sociopolitical process of Imperialism !! Since in late inception, it has been used in many

applications. Has shown good convergence and global minimum

achievement. Has a lot to do with.

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Colonial Competitive Algorithm!? Is it useful?

A short list of CCA applications SISO PID Controller Design MIMO PID Controller design for Distillation Column

Process Intelligent Recommender Systems Adaptive Antenna Design Optimal Layout design Nash Equilibrium point achievement Gershgorin Bands Narrowing Automated Guided Vehicle Materials property characterization through sharp and

spherical indentation tests. …

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What is Colonial Competitive Algorithm?

Basic Idea of CCA

GAs use the biological evolution of human as a source of inspiration.

Why most of evolutionary algorithms such as GA and SA are computer simulation of natural processes?

Is human evolution limmited to biological evolution? No!! Are there another kinds of evolution? Yes.! Is there any way to use these kind evolutions as a

sourse of inspiration for an optimization algorithm? Yes.

Colonial Competitive Algorithm (CCA)

Is one of the answers to this question

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What is Colonial Competitive Algorithm?

Basic Idea of CCA

Imperialism is the policy of extending the power and rule of a government beyond its own boundaries.

A country may attempt to dominate others by direct rule or by less obvious means such as a control of markets for goods or raw materials. The latter is often called neocolonialism.

Imperialism changed the public attitude toward civilization of the West during 19th and 20th century.

Social Darwinists interpreted imperialism and supported the idea that the culture of West is superior to the East’s culture.!

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What is Colonial Competitive Algorithm? Basic idea of CCA

According to the assimilation policy, some countries like France intended to construct a new France in Indochina through building French speaking schools and expanding its language and culture.

In the proposed algorithm, the imperialists do the same for their colonies. !!!

All the imperialists compete for taking possession of colonies of each other.

Also assimilation policy is modeled by moving the colonies toward the imperialists.

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What is Colonial Competitive Algorithm?

A big picture

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We form an array of variable values to be optimized.

In GA terminology, this array is called “chromosome”, but here the term “country” is used for this array.

We are looking for the best country. That is a country with best Culture, Language, … !

What is Colonial Competitive Algorithm?

Creating Initial Empires

1 2 3[ , , ,..., ]varNcountry p p p p

var1 2 3( ) ( , , ,..., )Ncost f country f p p p p

Culture Economical Policy Language Religion…..

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What is Colonial Competitive Algorithm?

Generating Initial Empires (Cont.)

max{ }n n ii

C c c

1

imp

nn N

ii

Cp

C

. . { . }n n colN C round p N

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What is Colonial Competitive Algorithm?

A big picture

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What is Colonial Competitive Algorithm? Assimilation Policy!

Culture

Language

Imperialist states started to spread their culture in their colonies through making the schools with their own language and ...

(0 , )x U d

Revolution

A sudden change in socio-political characteristics of a country

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What is Colonial Competitive Algorithm?

A big picture

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What is Colonial Competitive Algorithm? Exchanging Positions of the Imperialist and a Colony

While moving toward the imperialist, a colony may reach to a position with lower cost than that of imperialist.

In such a case, the imperialist moves to the position of that colony and vise versa.

Imperialist

Best Colony

Imperialist

Colony

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What is Colonial Competitive Algorithm?

A big picture

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What is Colonial Competitive Algorithm?

Total Power of an Empire

Total power of an empire is mainly affected by the power of imperialist country.

But the power of the colonies of an empire has an effect, albeit negligible, on the total power of that empire.

This fact is modeled by defining the total cost as

. . ( ) { ( )}n n n

T C Cost imperialist mean Cost colonies of empire

. . ( ) { ( )}n n n

T C Cost imperialist mean Cost colonies of empire

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What is Colonial Competitive Algorithm?

A big picture

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What is Colonial Competitive Algorithm?

Imperialistic Competition all empires try to take possession of colonies of other

empires and control them.

Imperialist 1

Imperialist 2

Imperialist 3

Imperialist N

Empire 1

Empire 2

Empire 3

Empire N

The Weakest EmpireWeakest Colony in

Weakest Empire

2P

3P

NP

. . . .

. . . .

.

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What is Colonial Competitive Algorithm?

Imperialistic Competition (Cont.)

. . . . . max{ . . }n n i

i

N T C T C T C

1

. . .

. . .n imp

n

p N

i

i

N T Cp

N T C

1 2 3

, , , ...,Nimp

p p p pp p p p

P1 2 3, , , ...,

impN

r r r r R

1 2 3, , , ..., (0,1)

impN

r r r r U

1 2 3, , , ...,

impN

D D D D D = P - R

1 2 31 2 3, , , ... ,

N impimpp p p p N

p r p r p r p r =

Maximum?

Roulette Wheel?

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What is Colonial Competitive Algorithm?

A big picture

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What is Colonial Competitive Algorithm?

Pseudo Code Select some random points on the function and initialize the

empires. Move the colonies toward their relevant imperialist

(Assimilating). If there is a colony in an empire which has lower cost than that

of imperialist, exchange the positions of that colony and the imperialist.

Compute the total cost of all empires (Related to the power of both imperialist and its colonies).

Pick the weakest colony (colonies) from the weakest empire and give it (them) to the empire that has the most likelihood to possess it (Imperialistic competition).

Eliminate the powerless empires. If there is just one empire, stop, if not go to 2.

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Simulation Results 2*2 MIMO Distillation Column

3

7 3

12.8 18.9( ) ( )1 16.7 1 21

.( ) ( )6.6 19.4

1 10.9 1 14.4

s s

Ds s

B

e eX s R ss s

X s S se e

s s

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Simulation Results

Wang, Q. G., Zou, B., Lee, T. H., & Qiang, B. (1997). Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica, 33(3), pp 319–330.

1 10.18 0.047 0.01 0.023 0.008

1 10.067 0.016 0.054 0.07 0.016

( )

ss s

ss s

s

C

11 11 12 12 12

21 21 21 22 22

1 1

( )1 1

P I P I D

P I D P I

K K K K K ss s

s

K K K s K Ks s

C

11 12 21 220 0 0 0

11 12 21 22

( ) ( ) ( ) ( )IAE e t dt e t dt e t dt e t dt

IAE IAE IAE IAE

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Simulation Results Schematics

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Simulation Results Convergence

the steady state convergence value of CCA is 12.8549, which is smaller than that of GA, 14. 9334.

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Simulation Results Resulting Controllers

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Simulation Results Step Responses

Output 1

Output 2

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Simulation Results Step Responses (Cont.)

Error Output 1

Error Output 2

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Simulation Results Comparing

The controlller obtained by CCA has generally better performance than the others.

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Conclusion

Colonial Competitive Algorithm is a novel evolutionary optimization algorithm.

It has successfully been used to solve some optimization problems.

It is based on the sociopolitical evolution of human.

It was able to properly tune the PID parameters for a MIMO

It has a lot to do with.

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The end Thanks

Thanks for your

attention!

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